OFFSET
3,1
COMMENTS
This includes intersection points outside of the n-gon. Note that for odd n, n divides a(n); for even n, n divides a(n)-1. For odd n, it appears that a(n)=n(n^3-7n^2+15n-1)/8.
That formula is correct: see the Sidorenko link. - N. J. A. Sloane, Sep 12 2021
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 3..100
T. D. Noe, Pentagon Illustrated
J. F. Rigby, Multiple intersections of diagonals of regular polygons, and related topics, Geom. Dedicata 9 (1980), 207-238.
Scott R. Shannon, Image for n = 3. In this and other images the dots showing the regular n-gon's vertices are slightly larger and circled with white for clarity. The dot color key is at the top-left of the image.
Scott R. Shannon, Image for n = 4.
Scott R. Shannon, Image for n = 5.
Scott R. Shannon, Image for n = 6.
Scott R. Shannon, Image for n = 7.
Scott R. Shannon, Image for n = 8.
Scott R. Shannon, Image for n = 9.
Scott R. Shannon, Image for n = 10.
Scott R. Shannon, Image for n = 11.
Scott R. Shannon, Image for n = 12.
Alexander Sidorenko, Explicit Formulas for Odd-Indexed Terms in A344899, A146212, and A344857.
FORMULA
There is a formula for odd n: see Comment section and the Sidorenko link. - N. J. A. Sloane, Sep 12 2021
EXAMPLE
a(5)=15 because there are 5 points inside the pentagon, 5 points on the pentagon and five points outside of the pentagon.
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
T. D. Noe, Oct 28 2008
EXTENSIONS
More terms from Jon E. Schoenfield, Nov 10 2008
STATUS
approved